Question

The value of sin[tan⁻¹(-√3)+cos⁻¹(- √3/2)] is......,Select Proper option from the given options.
(a) -1
(b) 0
(c) 1/2
(d) 1

Answer 1

we have to find the value of sin[tan^-1(-√3) + cos^-1(-√3/2)]

we know, tan^-1(-x) = -tan^-1x
and cos^-1(-x) =π - cos^-1x

so, sin[tan^-1(-√3) + cos^-1(-√3/2)] = sin[-tan^-1(√3) + π - cos^-1(√3/2)]

we also know , tan^-1(√3) = π/3
cos^-1(√3/2) = π/6

so, sin[-tan^-1(√3) + π - cos^-1(√3/2)] = sin[-π/3 + π - π/6 ]

= sin[ 2π/3 - π/6 ]

= sin[π/2]

= 1

hence, option (d) is correct.